If the 555 circuit is working correctly, and you can vary it the way you want, and the only problem is that its output is a square wave rather than a triangle or sawtooth wave, take the output from pin 2/6, the top of the timing capacitor. This has a modified triangle wave on it and its amplitude is a constant regardless of frequency. However, this is not a low impedance output like pin 3 is and it is not as loud. Connect it to you amplifier input and see what you think of the sound.
A pure triangle wave has twice as many harmonics as a square wave, but they drop off in amplitude more quickly as the harmonic frequency increases.
ak